Web hosting, DSL, and domain names

[scott at MIT.EDU (Scott R Ehrlich)]

I have a domain name registered with a web hosting provider.   The domain name
has an associated IP address as assigned by the hosting provider.   If I were
to eventually switch from cable modem service to DSL via speakeasy, for
example, would I be able to "share" my domain name and IP on my line if I
wanted to let the hosting provider continue to host my domain name?    The
provider is reliable and, for the money, can do a lot more for me than I could
on my own.    I also have confidence in their server management.

It would be nice to start up something like Thunderbird to both read and send
email  under my domain name without a mail server complaining relaying is not
allowed.

I do know it is possible to have multiple IPs pointing to the same host.   Could
that work for my potential scenario?   The hosting provider maintains the name
and IP, and I get assigned an IP which is also resolvable to the domain?

Thanks.

Scott